Russia poses a danger to the U.S. and must be held accountable for its actions, Rex Tillerson, President-elect Donald Trump’s nominee for secretary of state and the former CEO of Exxon Mobil Corp., told senators at his confirmation hearing.

“Our NATO allies are right to be alarmed at a resurgent Russia,” Tillerson, 64, said before the Senate Foreign Relations Committee on Wednesday. At the same time, he faulted a lack of U.S. leadership for Russia’s aggressiveness, citing “weak or...